Naturally saturated fats are excellent for health, are heat resistant and don't oxidize at room temp. Their shelf-life is therefore quite long. Extra virgin coconut oil is one of them. Lard, ghee, tallow, etc, are other excellent sources.

Poly-unsat fats are usually not good except DHA and EPA or omega-3' (and ALA but this one is not that useful) which are found in abundance in oily fish (mackerel, sardines, anchovies, salmon, etc). Poly means that these oils are VERY unstable, do not tolerate heat and oxidize fast. That's bad. Omega-6 fat is also good to some extenet but the target is to get 1:1 ratio between 3's and 6's. The problem is that western diets are full of 6's and poor in 3's. Moreover, the sources of these 6's is processed vegetable oil like safflower oil, etc, which are known to be quite unhealthy (already half rancid when you buy them, and frying with them is a cooking blasphemy! and they are ubiquitous, found in about every processed food).

Mono-unsat are good, we need them. Make sure your sources are high quality (macademia oil, olive oil, etc). But don't fry with them as they are not as heat resistant as sat fats. They are great in salad dressing, mayonnaise, etc.

I forgot: trans-fats. Run away from them. They are unsat fats that were artificially saturated. A real health hazard, nothing to do with naturally sat fats.